Changeset 6625 for branches/UKMO/dev_r5518_v3.4_asm_nemovar_community/DOC/TexFiles/Chapters/Chap_LDF.tex
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branches/UKMO/dev_r5518_v3.4_asm_nemovar_community/DOC/TexFiles/Chapters/Chap_LDF.tex
r6617 r6625 1 1 2 2 % ================================================================ 3 % Chapter ———Lateral Ocean Physics (LDF)3 % Chapter � Lateral Ocean Physics (LDF) 4 4 % ================================================================ 5 5 \chapter{Lateral Ocean Physics (LDF)} … … 68 68 When none of the \textbf{key\_dynldf\_...} and \textbf{key\_traldf\_...} keys are 69 69 defined, a constant value is used over the whole ocean for momentum and 70 tracers, which is specified through the \np{rn\_ahm \_0\_lap} and \np{rn\_aht\_0} namelist70 tracers, which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist 71 71 parameters. 72 72 … … 77 77 mixing coefficients will require 3D arrays. In the 1D option, a hyperbolic variation 78 78 of the lateral mixing coefficient is introduced in which the surface value is 79 \np{rn\_aht \_0} (\np{rn\_ahm\_0\_lap}), the bottom value is 1/4 of the surface value,79 \np{rn\_aht0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value, 80 80 and the transition takes place around z=300~m with a width of 300~m 81 81 ($i.e.$ both the depth and the width of the inflection point are set to 300~m). … … 93 93 \end{equation} 94 94 where $e_{max}$ is the maximum of $e_1$ and $e_2$ taken over the whole masked 95 ocean domain, and $A_o^l$ is the \np{rn\_ahm \_0\_lap} (momentum) or \np{rn\_aht\_0} (tracer)95 ocean domain, and $A_o^l$ is the \np{rn\_ahm0} (momentum) or \np{rn\_aht0} (tracer) 96 96 namelist parameter. This variation is intended to reflect the lesser need for subgrid 97 97 scale eddy mixing where the grid size is smaller in the domain. It was introduced in … … 105 105 Other formulations can be introduced by the user for a given configuration. 106 106 For example, in the ORCA2 global ocean model (see Configurations), the laplacian 107 viscosity operator uses \np{rn\_ahm \_0\_lap}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$108 north and south and decreases linearly to \np{rn\_aht \_0}~= 2.10$^3$ m$^2$/s107 viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ 108 north and south and decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s 109 109 at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}. This modification 110 110 can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. … … 120 120 \subsubsection{Space and Time Varying Mixing Coefficients} 121 121 122 There are no default specifications of space and time varying mixing coefficient. One 123 available case is specific to the ORCA2 and ORCA05 global ocean configurations. It 124 provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both 125 iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of 126 baroclinic instability. This specification is actually used when an ORCA key 122 There is no default specification of space and time varying mixing coefficient. 123 The only case available is specific to the ORCA2 and ORCA05 global ocean 124 configurations. It provides only a tracer 125 mixing coefficient for eddy induced velocity (ORCA2) or both iso-neutral and 126 eddy induced velocity (ORCA05) that depends on the local growth rate of 127 baroclinic instability. This specification is actually used when an ORCA key 127 128 and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 128 129 \subsubsection{Smagorinsky viscosity (\key{dynldf\_c3d} and \key{dynldf\_smag})}130 131 The \key{dynldf\_smag} key activates a 3D, time-varying viscosity that depends on the132 resolved motions. Following \citep{Smagorinsky_93} the viscosity coefficient is set133 proportional to a local deformation rate based on the horizontal shear and tension,134 namely:135 136 \begin{equation}137 A_{m_{Smag}} = \left(\frac{{\sf CM_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert138 \end{equation}139 140 \noindent where the deformation rate $\vert{D}\vert$ is given by141 142 \begin{equation}143 \vert{D}\vert=\sqrt{\left({\frac{\partial{u}} {\partial{x}}}144 -{\frac{\partial{v}} {\partial{y}}}\right)^2145 + \left({\frac{\partial{u}} {\partial{y}}}146 +{\frac{\partial{v}} {\partial{x}}}\right)^2}147 \end{equation}148 149 \noindent and $L$ is the local gridscale given by:150 151 \begin{equation}152 L^2 = \frac{2{e_1}^2 {e_2}^2}{\left ( {e_1}^2 + {e_2}^2 \right )}153 \end{equation}154 155 \citep{Griffies_Hallberg_MWR00} suggest values in the range 2.2 to 4.0 of the coefficient156 $\sf CM_{Smag}$ for oceanic flows. This value is set via the \np{rn\_cmsmag\_1} namelist157 parameter. An additional parameter: \np{rn\_cmsh} is included in NEMO for experimenting158 with the contribution of the shear term. A value of 1.0 (the default) calculates the159 deformation rate as above; a value of 0.0 will discard the shear term entirely.160 161 For numerical stability, the calculated viscosity is bounded according to the following:162 163 \begin{equation}164 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_ahm\_m\_lap\right ) \geq A_{m_{Smag}}165 \geq rn\_ahm\_0\_lap166 \end{equation}167 168 \noindent with both parameters for the upper and lower bounds being provided via the169 indicated namelist parameters.170 171 \bigskip When $ln\_dynldf\_bilap = .true.$, a biharmonic version of the Smagorinsky172 viscosity is also available which sets a coefficient for the biharmonic viscosity as:173 174 \begin{equation}175 B_{m_{Smag}} = - \left(\frac{{\sf CM_{bSmag}}}{\pi}\right)^2 {L^4\over 8}\vert{D}\vert176 \end{equation}177 178 \noindent which is bounded according to:179 180 \begin{equation}181 {\rm MAX}\left (-{ L^4\over {64\Delta{t}}}, rn\_ahm\_m\_blp\right ) \leq B_{m_{Smag}}182 \leq rn\_ahm\_0\_blp183 \end{equation}184 185 \noindent Note the reversal of the inequalities here because NEMO requires the biharmonic186 coefficients as negative numbers. $\sf CM_{bSmag}$ is set via the \np{rn\_cmsmag\_2}187 namelist parameter and the bounding values have corresponding entries in the namelist too.188 189 \bigskip The current implementation in NEMO also allows for 3D, time-varying diffusivities190 to be set using the Smagorinsky approach. Users should note that this option is not191 recommended for many applications since diffusivities will tend to be largest near192 boundaries (where shears are greatest) leading to spurious upwellings193 (\citep{Griffies_Bk04}, chapter 18.3.4). Nevertheless the option is there for those194 wishing to experiment. This choice requires both \key{traldf\_c3d} and \key{traldf\_smag}195 and uses the \np{rn\_chsmag} (${\sf CH_{Smag}}$), \np{rn\_smsh} and \np{rn\_aht\_m}196 namelist parameters in an analogous way to \np{rn\_cmsmag\_1}, \np{rn\_cmsh} and197 \np{rn\_ahm\_m\_lap} (see above) to set the diffusion coefficient:198 199 \begin{equation}200 A_{h_{Smag}} = \left(\frac{{\sf CH_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert201 \end{equation}202 203 204 For numerical stability, the calculated diffusivity is bounded according to the following:205 206 \begin{equation}207 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_aht\_m\right ) \geq A_{h_{Smag}}208 \geq rn\_aht\_0209 \end{equation}210 211 212 129 213 130 $\ $\newline % force a new ligne … … 227 144 (3) for isopycnal diffusion on momentum or tracers, an additional purely 228 145 horizontal background diffusion with uniform coefficient can be added by 229 setting a non zero value of \np{rn\_ahmb \_0} or \np{rn\_ahtb\_0}, a background horizontal146 setting a non zero value of \np{rn\_ahmb0} or \np{rn\_ahtb0}, a background horizontal 230 147 eddy viscosity or diffusivity coefficient (namelist parameters whose default 231 148 values are $0$). However, the technique used to compute the isopycnal
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